Continuum fallacy

The use of the fact of continuity between them to throw doubt on a real difference between two things

Example

Example a room is never either "hot" or "cold", because of the continuum of temperatures. The fallacy causes one to erroneously reject a vague claim simply because it is not as precise as one would like it to be. Vagueness alone does not necessarily imply invalidity.

Form

Treatment

Dealt with by pointing out that the difference is nevertheless real. This again may be made stronger by pointing out that application of the same method of argument would deny the difference between "black" and "white" or between "hot" and "cold".